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Ample D4-D2-D0 Decay

Evgeny Andriyash, Gregory W. Moore

TL;DR

This work demonstrates that the large-radius BPS index Ω(Γ; t) for D4-D2-D0 states on a Calabi–Yau threefold is deeply chamber-dependent and can undergo substantial wall-crossing, even dominating single-centered BH entropy in certain multicentered configurations. It constructs an explicit three-centered boundstate whose MS wall extends to infinity, showing ΔΩ can exceed the single-centered BH contribution and thereby challenging the weak-coupling OSV conjecture in generic chambers. The paper then analyzes the M-theory lift and a near-horizon λ-deformation, concluding that the three-centered solution does not yield a single AdS$_3\times S^2$ boundary, which informs holographic interpretations and motivates conjectures linking AdS-point attractor trees to multicentered flows. Finally, it proposes conjectures (SAFC-based) about the relation between moduli-space components, asymptotic separations, and holographic duals, offering a refined perspective on the OSV program and modularity of BPS index generating functions in multi-parameter settings.

Abstract

We study the wall-crossing behavior of the index of BPS states for D4-D2-D0 brane systems on a Calabi-Yau 3-fold at large radius and point out that not only is the ``BPS index at large radius'' chamber-dependent, but that the changes in the index can be large in the sense that they dominate single-centered black hole entropy. We discuss implications for the weak coupling OSV conjecture. We also analyze the near horizon limit of multicentered solutions, introduced in arXiv:0802.2257, for these particular configurations and comment on a general criterion, conjectured in arXiv:0802.2257, which identifies those multicentered solutions whose near horizon limit corresponds to a geometry with a single asymptotic AdS_3 x S^2 boundary.

Ample D4-D2-D0 Decay

TL;DR

This work demonstrates that the large-radius BPS index Ω(Γ; t) for D4-D2-D0 states on a Calabi–Yau threefold is deeply chamber-dependent and can undergo substantial wall-crossing, even dominating single-centered BH entropy in certain multicentered configurations. It constructs an explicit three-centered boundstate whose MS wall extends to infinity, showing ΔΩ can exceed the single-centered BH contribution and thereby challenging the weak-coupling OSV conjecture in generic chambers. The paper then analyzes the M-theory lift and a near-horizon λ-deformation, concluding that the three-centered solution does not yield a single AdS boundary, which informs holographic interpretations and motivates conjectures linking AdS-point attractor trees to multicentered flows. Finally, it proposes conjectures (SAFC-based) about the relation between moduli-space components, asymptotic separations, and holographic duals, offering a refined perspective on the OSV program and modularity of BPS index generating functions in multi-parameter settings.

Abstract

We study the wall-crossing behavior of the index of BPS states for D4-D2-D0 brane systems on a Calabi-Yau 3-fold at large radius and point out that not only is the ``BPS index at large radius'' chamber-dependent, but that the changes in the index can be large in the sense that they dominate single-centered black hole entropy. We discuss implications for the weak coupling OSV conjecture. We also analyze the near horizon limit of multicentered solutions, introduced in arXiv:0802.2257, for these particular configurations and comment on a general criterion, conjectured in arXiv:0802.2257, which identifies those multicentered solutions whose near horizon limit corresponds to a geometry with a single asymptotic AdS_3 x S^2 boundary.

Paper Structure

This paper contains 7 sections, 72 equations, 4 figures.

Table of Contents

  1. Introduction and Conclusion
  2. Some general remarks on stability at large radius
  3. An example
  4. Comparison of the entropies
  5. M-theory lift and its near-horizon limit
  6. Some general remarks on holographic duals of $D4D4$ boundstates.
  7. Attractor flow trees

Figures (4)

  • Figure 1: The two contributing topologies of attractor trees. The left tree is the main example of this paper. The right tree also exists, for our charges, in certain regions of moduli space.
  • Figure 2: The two intervals, corresponding to topologies of Figure 1.
  • Figure 3: The behavior of the flow for the first edge of the tree.
  • Figure 4: An example of attractor flow tree.